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Question 1058425: Total profit P is the difference between total revenue R and total cost C. Given the following total-revenue and total-cost functions, find the total profit, the maximum value of the total profit, and the value of x at which it occurs..
R(x)= 1200x-(x squared)
C(x)= 3100+20x
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! The profit function is:
P(x) = R(x) - C(x)
P(x) = (1200x - x^2) - (3100 + 20x)
P(x) = -x^2 + 1200x - 20x - 3100
P(x) = -x^2 + 1180x - 3100
This is the equation of a parabola that opens downward. The maximum value of the profit
corresponds to the vertex of the parabola.
The x-coordinate of the vertex is:
x = -b/2a = (-1180) / (-1*2) = 590
The function value at the vertex is then:
P(590) = -(590)^2 + 1198(590) - 3100
P(590) = 345,000
Solution:
Total profit = -x^2 + 1180x - 3100
Maximum profit = 345,000, at x = 590
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